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Statistics 9-12 / Week 05 / Track Day
6/6
Week 05 · Correlation and Causation

Track Day

Track Day: together, not because of
// How tight is the cloud, and what it does not prove
⏱ about 20 min

Track Day: Together, Not Because Of

Saturday, the kitchen table again, with graph paper and the Run Log.

"Pick two numbers that might go together," Comet says. "Minutes the tap runs and cups filled. Pages read and minutes spent."

The family picks pages and minutes and collects six pairs. Wren plots them. "What do you notice?"

"Tight and rising," someone says. "r near 1?"

"By eye, strong positive," Wren says. "Now the careful sentence. Do minutes cause pages, or pages cause minutes?"

"Together," Comet says. "Reading more pages takes more minutes. Both are the same reading, really."

Nova hovers over the plot. "Would you like a hint? Say what you saw, not what you believe."

  1. r measures how tightly dots follow a straight line, from -1 to 1. Sign is direction, size is strength.
  2. Strong is 0.7 or more. Under 0.3 is little or none, the range chance alone can reach.
  3. r is the average of the products of the x and y z-scores. Technology computes it; you read it.
  4. r misses curves and says nothing about slope size or units.
  5. Correlation is not causation. Name the lurking variable. Only a randomized experiment shows a cause.
◇ FAMILY CORRELATION
Choose two numbers that might go together and collect at least six pairs. Write them in a table.
Plot the dots. Take turns guessing r by eye: strong, weak or little, positive or negative.
If you have a calculator or spreadsheet, find r and compare it with your guesses.
Together, write one careful sentence: "In our table, more x went with more y." No "makes" allowed.
Name one lurking variable that could drive both numbers.
For a grown-up
Any timing or walking is on a safe path, never a road, with you aware and water at hand.
Help your learner find r on a calculator or spreadsheet if one is handy. By eye is fine too.
Ask them to explain why "together" is not "because of". That conversation is the goal.
ONE MORE CAREFUL READING
  • Read the question.
  • Tap your answer.
A scatter plot, Two tokens, reshuffled, first token across and second token up, with 8 points.Round 2 of the token lab gave r = 0.05. How would you describe the linear relationship?
Your family found that more pages went with more minutes and someone says pages cause minutes. Which statement is the careful one?
Is a strong r proof that x causes y? Type yes or no.
WHY THIS EXERCISEThis one-word answer is the most important thing the week teaches.
Draw your family scatter plot. Write your r by eye and your careful sentence under it.

A careful family. Next week: asking a sample of runners about the course, and what a sample can and cannot tell you.

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